English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $G$ be a semi-simple Lie group in the Harish-Chandra class with maximalcompact subgroup $K$. Let $\Omega_K$ be minus the radial Casimir operator. Let$\frac{1}{4} \dim(G/K) < S_G < \frac{1}{2} \dim(G/K) , s \in (0, S_G]$ and $p\in (1,\infty)$ be such that \[ \left| \frac{1}{p} - \frac{1}{2} \right| <\frac{s}{2 S_G}. \] Then, there exists a constant $C_{G,s,p} >0$ such that forevery $m \in L^\infty(G) \cap L^2(G)$ bi-$K$-invariant with $m \in {\rmDom}(\Omega_K^s)$ and $\Omega_K^s(m) \in L^{2S_G/s}(G)$ we have, \[ \Vert T_m:L^p(\widehat{G}) \rightarrow L^p(\widehat{G}) \Vert \leq C_{G, s,p} \Vert\Omega_K^s(m) \Vert_{L^{2S_G/s}(G)}, \] where $T_m$ is the Fourier multiplierwith symbol $m$ acting on the non-commutative $L^p$-space of the group vonNeumann algebra of $G$. This gives new examples of $L^p$-Fourier multiplierswith decay rates becoming slower when $p$ approximates $2$.

A Sobolev estimate for radial $L^p$-multipliers on a class of semi-simple Lie groups